A close friend's two daughters are Laura and Julia. She is expecting a little girl this fall and seeking another name that is a trend-defying classic, yet sophisticated and does not feel dated. A "little black dress" of names, if you will.
Maria, Eva, Lucy, and Clara were my first thoughts. I think Lydia would fit very well, too, although it does share an initial with Laura--I don't know if she's opposed to that or not. I also really find Jane, Catherine, Evelyn, and Eleanor to be "little black dress" names.